6x^2+35x-11=2x^2-2x

Solution for 6x^2+35x-11=2x^2-2x equation:

Simplifying
6x2 + 35x + -11 = 2x2 + -2x

Reorder the terms:
-11 + 35x + 6x2 = 2x2 + -2x

Reorder the terms:
-11 + 35x + 6x2 = -2x + 2x2

Solving
-11 + 35x + 6x2 = -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
-11 + 35x + 2x + 6x2 + -2x2 = -2x + 2x2 + 2x + -2x2

Combine like terms: 35x + 2x = 37x
-11 + 37x + 6x2 + -2x2 = -2x + 2x2 + 2x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-11 + 37x + 4x2 = -2x + 2x2 + 2x + -2x2

Reorder the terms:
-11 + 37x + 4x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
-11 + 37x + 4x2 = 0 + 2x2 + -2x2
-11 + 37x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-11 + 37x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.75 + 9.25x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 9.25x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 9.25x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 9.25x + x2 = 0 + 2.75
9.25x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
9.25x + x2 = 2.75

The x term is 9.25x.  Take half its coefficient (4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
9.25x + 21.390625 + x2 = 2.75 + 21.390625

Reorder the terms:
21.390625 + 9.25x + x2 = 2.75 + 21.390625

Combine like terms: 2.75 + 21.390625 = 24.140625
21.390625 + 9.25x + x2 = 24.140625

Factor a perfect square on the left side:
(x + 4.625)(x + 4.625) = 24.140625

Calculate the square root of the right side: 4.913311002

Break this problem into two subproblems by setting 
(x + 4.625) equal to 4.913311002 and -4.913311002.

Subproblem 1
x + 4.625 = 4.913311002

Simplifying
x + 4.625 = 4.913311002

Reorder the terms:
4.625 + x = 4.913311002

Solving
4.625 + x = 4.913311002

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = 4.913311002 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = 4.913311002 + -4.625
x = 4.913311002 + -4.625

Combine like terms: 4.913311002 + -4.625 = 0.288311002
x = 0.288311002

Simplifying
x = 0.288311002

Subproblem 2
x + 4.625 = -4.913311002

Simplifying
x + 4.625 = -4.913311002

Reorder the terms:
4.625 + x = -4.913311002

Solving
4.625 + x = -4.913311002

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = -4.913311002 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = -4.913311002 + -4.625
x = -4.913311002 + -4.625

Combine like terms: -4.913311002 + -4.625 = -9.538311002
x = -9.538311002

Simplifying
x = -9.538311002

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.288311002, -9.538311002}